Numerical and Analytic dissipativity of the theta-Method for Delay Differential Equations with a Bounded Variable Lag

This paper focuses on the analytic and numerical dissipativity of θ-method for delay differential equations with a bounded variable lag. A generalized Halanay inequality is derived, and a sufficient condition is presented to ensure that delay differential equations with a bounded variable lag are dissipative. We then apply θ-method to such delay differential equations, and investigate the numerical dissipativity of the θ-method.

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